Mathematic and Computational Models for Osseointegration in Titanium Dental Implants: A Systematic Review of Current Approaches and Future Directions.

PURPOSE: To identify, compare, and critically evaluate the main mathematic and computational models used to study osseointegration in titanium (Ti) dental implants. MATERIALS AND METHODS: A systematic literature search was conducted in MEDLINE/PubMed, Scopus, and SpringerLink databases up to February 2025. Studies were included if they employed mathematic or computational models-such as finite element analysis, mechanobiologic frameworks, or reactiondiffusion systems-to investigate osseointegration in Ti dental implants. This study focused on the predictive accuracy, biologic and mechanical integration, and clinical relevance of the main mathematic and computational models- highlighting their contributions and limitations in simulating implant stability and bone remodeling. A quality assessment of included studies was performed using the Grading of Recommendations, Assessment, Development and Evaluation (GRADE) approach to ensure methodologic rigor. RESULTS: A total of 42 studies met the inclusion criteria. Finite element analysis (FEA) was the most commonly used technique, primarily addressing mechanical aspects such as stress distribution and implant geometry. Mechanobiologic and reaction-diffusion models incorporated biologic and biochemical processes but lacked standardization and clinical validation. The integration of mechanical and biologic factors remained limited, hindering real-world applicability. Despite progress, only a few models included patient-specific parameters or were validated experimentally. CONCLUSIONS: Mathematic and computational models have substantially advanced our understanding of osseointegration in Ti dental implants. However, their translation into clinical practice is still constrained by validation gaps, heterogeneity in model parameters, and limited biologic integration. Future research should emphasize hybrid models, incorporate robust validation protocols, and leverage artificial intelligence to enable personalized and clinically meaningful simulations.